/js/src/dtoa.c

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  1. /* -*- Mode: C; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */
  2. /****************************************************************
  3. *
  4. * The author of this software is David M. Gay.
  5. *
  6. * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
  7. *
  8. * Permission to use, copy, modify, and distribute this software for any
  9. * purpose without fee is hereby granted, provided that this entire notice
  10. * is included in all copies of any software which is or includes a copy
  11. * or modification of this software and in all copies of the supporting
  12. * documentation for such software.
  13. *
  14. * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
  15. * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
  16. * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
  17. * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
  18. *
  19. ***************************************************************/
  20. /* Please send bug reports to David M. Gay (dmg at acm dot org,
  21. * with " at " changed at "@" and " dot " changed to "."). */
  22. /* On a machine with IEEE extended-precision registers, it is
  23. * necessary to specify double-precision (53-bit) rounding precision
  24. * before invoking strtod or dtoa. If the machine uses (the equivalent
  25. * of) Intel 80x87 arithmetic, the call
  26. * _control87(PC_53, MCW_PC);
  27. * does this with many compilers. Whether this or another call is
  28. * appropriate depends on the compiler; for this to work, it may be
  29. * necessary to #include "float.h" or another system-dependent header
  30. * file.
  31. */
  32. /* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
  33. *
  34. * This strtod returns a nearest machine number to the input decimal
  35. * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
  36. * broken by the IEEE round-even rule. Otherwise ties are broken by
  37. * biased rounding (add half and chop).
  38. *
  39. * Inspired loosely by William D. Clinger's paper "How to Read Floating
  40. * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
  41. *
  42. * Modifications:
  43. *
  44. * 1. We only require IEEE, IBM, or VAX double-precision
  45. * arithmetic (not IEEE double-extended).
  46. * 2. We get by with floating-point arithmetic in a case that
  47. * Clinger missed -- when we're computing d * 10^n
  48. * for a small integer d and the integer n is not too
  49. * much larger than 22 (the maximum integer k for which
  50. * we can represent 10^k exactly), we may be able to
  51. * compute (d*10^k) * 10^(e-k) with just one roundoff.
  52. * 3. Rather than a bit-at-a-time adjustment of the binary
  53. * result in the hard case, we use floating-point
  54. * arithmetic to determine the adjustment to within
  55. * one bit; only in really hard cases do we need to
  56. * compute a second residual.
  57. * 4. Because of 3., we don't need a large table of powers of 10
  58. * for ten-to-e (just some small tables, e.g. of 10^k
  59. * for 0 <= k <= 22).
  60. */
  61. /*
  62. * #define IEEE_8087 for IEEE-arithmetic machines where the least
  63. * significant byte has the lowest address.
  64. * #define IEEE_MC68k for IEEE-arithmetic machines where the most
  65. * significant byte has the lowest address.
  66. * #define Long int on machines with 32-bit ints and 64-bit longs.
  67. * #define IBM for IBM mainframe-style floating-point arithmetic.
  68. * #define VAX for VAX-style floating-point arithmetic (D_floating).
  69. * #define No_leftright to omit left-right logic in fast floating-point
  70. * computation of dtoa.
  71. * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
  72. * and strtod and dtoa should round accordingly.
  73. * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
  74. * and Honor_FLT_ROUNDS is not #defined.
  75. * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
  76. * that use extended-precision instructions to compute rounded
  77. * products and quotients) with IBM.
  78. * #define ROUND_BIASED for IEEE-format with biased rounding.
  79. * #define Inaccurate_Divide for IEEE-format with correctly rounded
  80. * products but inaccurate quotients, e.g., for Intel i860.
  81. * #define NO_LONG_LONG on machines that do not have a "long long"
  82. * integer type (of >= 64 bits). On such machines, you can
  83. * #define Just_16 to store 16 bits per 32-bit Long when doing
  84. * high-precision integer arithmetic. Whether this speeds things
  85. * up or slows things down depends on the machine and the number
  86. * being converted. If long long is available and the name is
  87. * something other than "long long", #define Llong to be the name,
  88. * and if "unsigned Llong" does not work as an unsigned version of
  89. * Llong, #define #ULLong to be the corresponding unsigned type.
  90. * #define KR_headers for old-style C function headers.
  91. * #define Bad_float_h if your system lacks a float.h or if it does not
  92. * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
  93. * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
  94. * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
  95. * if memory is available and otherwise does something you deem
  96. * appropriate. If MALLOC is undefined, malloc will be invoked
  97. * directly -- and assumed always to succeed. Similarly, if you
  98. * want something other than the system's free() to be called to
  99. * recycle memory acquired from MALLOC, #define FREE to be the
  100. * name of the alternate routine. (Unless you #define
  101. * NO_GLOBAL_STATE and call destroydtoa, FREE or free is only
  102. * called in pathological cases, e.g., in a dtoa call after a dtoa
  103. * return in mode 3 with thousands of digits requested.)
  104. * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
  105. * memory allocations from a private pool of memory when possible.
  106. * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
  107. * unless #defined to be a different length. This default length
  108. * suffices to get rid of MALLOC calls except for unusual cases,
  109. * such as decimal-to-binary conversion of a very long string of
  110. * digits. The longest string dtoa can return is about 751 bytes
  111. * long. For conversions by strtod of strings of 800 digits and
  112. * all dtoa conversions in single-threaded executions with 8-byte
  113. * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
  114. * pointers, PRIVATE_MEM >= 7112 appears adequate.
  115. * #define MULTIPLE_THREADS if the system offers preemptively scheduled
  116. * multiple threads. In this case, you must provide (or suitably
  117. * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
  118. * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
  119. * in pow5mult, ensures lazy evaluation of only one copy of high
  120. * powers of 5; omitting this lock would introduce a small
  121. * probability of wasting memory, but would otherwise be harmless.)
  122. * You must also invoke freedtoa(s) to free the value s returned by
  123. * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
  124. * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
  125. * avoids underflows on inputs whose result does not underflow.
  126. * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
  127. * floating-point numbers and flushes underflows to zero rather
  128. * than implementing gradual underflow, then you must also #define
  129. * Sudden_Underflow.
  130. * #define USE_LOCALE to use the current locale's decimal_point value.
  131. * #define SET_INEXACT if IEEE arithmetic is being used and extra
  132. * computation should be done to set the inexact flag when the
  133. * result is inexact and avoid setting inexact when the result
  134. * is exact. In this case, dtoa.c must be compiled in
  135. * an environment, perhaps provided by #include "dtoa.c" in a
  136. * suitable wrapper, that defines two functions,
  137. * int get_inexact(void);
  138. * void clear_inexact(void);
  139. * such that get_inexact() returns a nonzero value if the
  140. * inexact bit is already set, and clear_inexact() sets the
  141. * inexact bit to 0. When SET_INEXACT is #defined, strtod
  142. * also does extra computations to set the underflow and overflow
  143. * flags when appropriate (i.e., when the result is tiny and
  144. * inexact or when it is a numeric value rounded to +-infinity).
  145. * #define NO_ERRNO if strtod should not assign errno = ERANGE when
  146. * the result overflows to +-Infinity or underflows to 0.
  147. * #define NO_GLOBAL_STATE to avoid defining any non-const global or
  148. * static variables. Instead the necessary state is stored in an
  149. * opaque struct, DtoaState, a pointer to which must be passed to
  150. * every entry point. Two new functions are added to the API:
  151. * DtoaState *newdtoa(void);
  152. * void destroydtoa(DtoaState *);
  153. */
  154. #ifndef Long
  155. #define Long long
  156. #endif
  157. #ifndef ULong
  158. typedef unsigned Long ULong;
  159. #endif
  160. #ifdef DEBUG
  161. #include "stdio.h"
  162. #define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
  163. #endif
  164. #include "stdlib.h"
  165. #include "string.h"
  166. #ifdef USE_LOCALE
  167. #include "locale.h"
  168. #endif
  169. #ifdef MALLOC
  170. #ifdef KR_headers
  171. extern char *MALLOC();
  172. #else
  173. extern void *MALLOC(size_t);
  174. #endif
  175. #else
  176. #define MALLOC malloc
  177. #endif
  178. #ifndef FREE
  179. #define FREE free
  180. #endif
  181. #ifndef Omit_Private_Memory
  182. #ifndef PRIVATE_MEM
  183. #define PRIVATE_MEM 2304
  184. #endif
  185. #define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
  186. #endif
  187. #undef IEEE_Arith
  188. #undef Avoid_Underflow
  189. #ifdef IEEE_MC68k
  190. #define IEEE_Arith
  191. #endif
  192. #ifdef IEEE_8087
  193. #define IEEE_Arith
  194. #endif
  195. #include "errno.h"
  196. #ifdef Bad_float_h
  197. #ifdef IEEE_Arith
  198. #define DBL_DIG 15
  199. #define DBL_MAX_10_EXP 308
  200. #define DBL_MAX_EXP 1024
  201. #define FLT_RADIX 2
  202. #endif /*IEEE_Arith*/
  203. #ifdef IBM
  204. #define DBL_DIG 16
  205. #define DBL_MAX_10_EXP 75
  206. #define DBL_MAX_EXP 63
  207. #define FLT_RADIX 16
  208. #define DBL_MAX 7.2370055773322621e+75
  209. #endif
  210. #ifdef VAX
  211. #define DBL_DIG 16
  212. #define DBL_MAX_10_EXP 38
  213. #define DBL_MAX_EXP 127
  214. #define FLT_RADIX 2
  215. #define DBL_MAX 1.7014118346046923e+38
  216. #endif
  217. #ifndef LONG_MAX
  218. #define LONG_MAX 2147483647
  219. #endif
  220. #else /* ifndef Bad_float_h */
  221. #include "float.h"
  222. #endif /* Bad_float_h */
  223. #ifndef __MATH_H__
  224. #include "math.h"
  225. #endif
  226. #ifdef __cplusplus
  227. extern "C" {
  228. #endif
  229. #ifndef CONST
  230. #ifdef KR_headers
  231. #define CONST /* blank */
  232. #else
  233. #define CONST const
  234. #endif
  235. #endif
  236. #if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
  237. Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
  238. #endif
  239. typedef union { double d; ULong L[2]; } U;
  240. #define dval(x) ((x).d)
  241. #ifdef IEEE_8087
  242. #define word0(x) ((x).L[1])
  243. #define word1(x) ((x).L[0])
  244. #else
  245. #define word0(x) ((x).L[0])
  246. #define word1(x) ((x).L[1])
  247. #endif
  248. /* The following definition of Storeinc is appropriate for MIPS processors.
  249. * An alternative that might be better on some machines is
  250. * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
  251. */
  252. #if defined(IEEE_8087) + defined(VAX)
  253. #define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
  254. ((unsigned short *)a)[0] = (unsigned short)c, a++)
  255. #else
  256. #define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
  257. ((unsigned short *)a)[1] = (unsigned short)c, a++)
  258. #endif
  259. /* #define P DBL_MANT_DIG */
  260. /* Ten_pmax = floor(P*log(2)/log(5)) */
  261. /* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
  262. /* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
  263. /* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
  264. #ifdef IEEE_Arith
  265. #define Exp_shift 20
  266. #define Exp_shift1 20
  267. #define Exp_msk1 0x100000
  268. #define Exp_msk11 0x100000
  269. #define Exp_mask 0x7ff00000
  270. #define P 53
  271. #define Bias 1023
  272. #define Emin (-1022)
  273. #define Exp_1 0x3ff00000
  274. #define Exp_11 0x3ff00000
  275. #define Ebits 11
  276. #define Frac_mask 0xfffff
  277. #define Frac_mask1 0xfffff
  278. #define Ten_pmax 22
  279. #define Bletch 0x10
  280. #define Bndry_mask 0xfffff
  281. #define Bndry_mask1 0xfffff
  282. #define LSB 1
  283. #define Sign_bit 0x80000000
  284. #define Log2P 1
  285. #define Tiny0 0
  286. #define Tiny1 1
  287. #define Quick_max 14
  288. #define Int_max 14
  289. #ifndef NO_IEEE_Scale
  290. #define Avoid_Underflow
  291. #ifdef Flush_Denorm /* debugging option */
  292. #undef Sudden_Underflow
  293. #endif
  294. #endif
  295. #ifndef Flt_Rounds
  296. #ifdef FLT_ROUNDS
  297. #define Flt_Rounds FLT_ROUNDS
  298. #else
  299. #define Flt_Rounds 1
  300. #endif
  301. #endif /*Flt_Rounds*/
  302. #ifdef Honor_FLT_ROUNDS
  303. #define Rounding rounding
  304. #undef Check_FLT_ROUNDS
  305. #define Check_FLT_ROUNDS
  306. #else
  307. #define Rounding Flt_Rounds
  308. #endif
  309. #else /* ifndef IEEE_Arith */
  310. #undef Check_FLT_ROUNDS
  311. #undef Honor_FLT_ROUNDS
  312. #undef SET_INEXACT
  313. #undef Sudden_Underflow
  314. #define Sudden_Underflow
  315. #ifdef IBM
  316. #undef Flt_Rounds
  317. #define Flt_Rounds 0
  318. #define Exp_shift 24
  319. #define Exp_shift1 24
  320. #define Exp_msk1 0x1000000
  321. #define Exp_msk11 0x1000000
  322. #define Exp_mask 0x7f000000
  323. #define P 14
  324. #define Bias 65
  325. #define Exp_1 0x41000000
  326. #define Exp_11 0x41000000
  327. #define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
  328. #define Frac_mask 0xffffff
  329. #define Frac_mask1 0xffffff
  330. #define Bletch 4
  331. #define Ten_pmax 22
  332. #define Bndry_mask 0xefffff
  333. #define Bndry_mask1 0xffffff
  334. #define LSB 1
  335. #define Sign_bit 0x80000000
  336. #define Log2P 4
  337. #define Tiny0 0x100000
  338. #define Tiny1 0
  339. #define Quick_max 14
  340. #define Int_max 15
  341. #else /* VAX */
  342. #undef Flt_Rounds
  343. #define Flt_Rounds 1
  344. #define Exp_shift 23
  345. #define Exp_shift1 7
  346. #define Exp_msk1 0x80
  347. #define Exp_msk11 0x800000
  348. #define Exp_mask 0x7f80
  349. #define P 56
  350. #define Bias 129
  351. #define Exp_1 0x40800000
  352. #define Exp_11 0x4080
  353. #define Ebits 8
  354. #define Frac_mask 0x7fffff
  355. #define Frac_mask1 0xffff007f
  356. #define Ten_pmax 24
  357. #define Bletch 2
  358. #define Bndry_mask 0xffff007f
  359. #define Bndry_mask1 0xffff007f
  360. #define LSB 0x10000
  361. #define Sign_bit 0x8000
  362. #define Log2P 1
  363. #define Tiny0 0x80
  364. #define Tiny1 0
  365. #define Quick_max 15
  366. #define Int_max 15
  367. #endif /* IBM, VAX */
  368. #endif /* IEEE_Arith */
  369. #ifndef IEEE_Arith
  370. #define ROUND_BIASED
  371. #endif
  372. #ifdef RND_PRODQUOT
  373. #define rounded_product(a,b) a = rnd_prod(a, b)
  374. #define rounded_quotient(a,b) a = rnd_quot(a, b)
  375. #ifdef KR_headers
  376. extern double rnd_prod(), rnd_quot();
  377. #else
  378. extern double rnd_prod(double, double), rnd_quot(double, double);
  379. #endif
  380. #else
  381. #define rounded_product(a,b) a *= b
  382. #define rounded_quotient(a,b) a /= b
  383. #endif
  384. #define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
  385. #define Big1 0xffffffff
  386. #ifndef Pack_32
  387. #define Pack_32
  388. #endif
  389. #ifdef KR_headers
  390. #define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
  391. #else
  392. #define FFFFFFFF 0xffffffffUL
  393. #endif
  394. #ifdef NO_LONG_LONG
  395. #undef ULLong
  396. #ifdef Just_16
  397. #undef Pack_32
  398. /* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
  399. * This makes some inner loops simpler and sometimes saves work
  400. * during multiplications, but it often seems to make things slightly
  401. * slower. Hence the default is now to store 32 bits per Long.
  402. */
  403. #endif
  404. #else /* long long available */
  405. #ifndef Llong
  406. #define Llong long long
  407. #endif
  408. #ifndef ULLong
  409. #define ULLong unsigned Llong
  410. #endif
  411. #endif /* NO_LONG_LONG */
  412. #ifndef MULTIPLE_THREADS
  413. #define ACQUIRE_DTOA_LOCK(n) /*nothing*/
  414. #define FREE_DTOA_LOCK(n) /*nothing*/
  415. #endif
  416. #define Kmax 7
  417. struct
  418. Bigint {
  419. struct Bigint *next;
  420. int k, maxwds, sign, wds;
  421. ULong x[1];
  422. };
  423. typedef struct Bigint Bigint;
  424. #ifdef NO_GLOBAL_STATE
  425. #ifdef MULTIPLE_THREADS
  426. #error "cannot have both NO_GLOBAL_STATE and MULTIPLE_THREADS"
  427. #endif
  428. struct
  429. DtoaState {
  430. #define DECLARE_GLOBAL_STATE /* nothing */
  431. #else
  432. #define DECLARE_GLOBAL_STATE static
  433. #endif
  434. DECLARE_GLOBAL_STATE Bigint *freelist[Kmax+1];
  435. DECLARE_GLOBAL_STATE Bigint *p5s;
  436. #ifndef Omit_Private_Memory
  437. DECLARE_GLOBAL_STATE double private_mem[PRIVATE_mem];
  438. DECLARE_GLOBAL_STATE double *pmem_next
  439. #ifndef NO_GLOBAL_STATE
  440. = private_mem
  441. #endif
  442. ;
  443. #endif
  444. #ifdef NO_GLOBAL_STATE
  445. };
  446. typedef struct DtoaState DtoaState;
  447. #ifdef KR_headers
  448. #define STATE_PARAM state,
  449. #define STATE_PARAM_DECL DtoaState *state;
  450. #else
  451. #define STATE_PARAM DtoaState *state,
  452. #endif
  453. #define PASS_STATE state,
  454. #define GET_STATE(field) (state->field)
  455. static DtoaState *
  456. newdtoa(void)
  457. {
  458. DtoaState *state = (DtoaState *) MALLOC(sizeof(DtoaState));
  459. if (state) {
  460. memset(state, 0, sizeof(DtoaState));
  461. #ifndef Omit_Private_Memory
  462. state->pmem_next = state->private_mem;
  463. #endif
  464. }
  465. return state;
  466. }
  467. static void
  468. destroydtoa
  469. #ifdef KR_headers
  470. (state) STATE_PARAM_DECL
  471. #else
  472. (DtoaState *state)
  473. #endif
  474. {
  475. int i;
  476. Bigint *v, *next;
  477. for (i = 0; i <= Kmax; i++) {
  478. for (v = GET_STATE(freelist)[i]; v; v = next) {
  479. next = v->next;
  480. #ifndef Omit_Private_Memory
  481. if ((double*)v < GET_STATE(private_mem) ||
  482. (double*)v >= GET_STATE(private_mem) + PRIVATE_mem)
  483. #endif
  484. FREE((void*)v);
  485. }
  486. }
  487. FREE((void *)state);
  488. }
  489. #else
  490. #define STATE_PARAM /* nothing */
  491. #define STATE_PARAM_DECL /* nothing */
  492. #define PASS_STATE /* nothing */
  493. #define GET_STATE(name) name
  494. #endif
  495. static Bigint *
  496. Balloc
  497. #ifdef KR_headers
  498. (STATE_PARAM k) STATE_PARAM_DECL int k;
  499. #else
  500. (STATE_PARAM int k)
  501. #endif
  502. {
  503. int x;
  504. Bigint *rv;
  505. #ifndef Omit_Private_Memory
  506. size_t len;
  507. #endif
  508. ACQUIRE_DTOA_LOCK(0);
  509. /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
  510. /* but this case seems very unlikely. */
  511. if (k <= Kmax && (rv = GET_STATE(freelist)[k]))
  512. GET_STATE(freelist)[k] = rv->next;
  513. else {
  514. x = 1 << k;
  515. #ifdef Omit_Private_Memory
  516. rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
  517. #else
  518. len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
  519. /sizeof(double);
  520. if (k <= Kmax && GET_STATE(pmem_next) - GET_STATE(private_mem) + len <= PRIVATE_mem) {
  521. rv = (Bigint*)GET_STATE(pmem_next);
  522. GET_STATE(pmem_next) += len;
  523. }
  524. else
  525. rv = (Bigint*)MALLOC(len*sizeof(double));
  526. #endif
  527. rv->k = k;
  528. rv->maxwds = x;
  529. }
  530. FREE_DTOA_LOCK(0);
  531. rv->sign = rv->wds = 0;
  532. return rv;
  533. }
  534. static void
  535. Bfree
  536. #ifdef KR_headers
  537. (STATE_PARAM v) STATE_PARAM_DECL Bigint *v;
  538. #else
  539. (STATE_PARAM Bigint *v)
  540. #endif
  541. {
  542. if (v) {
  543. if (v->k > Kmax)
  544. FREE((void*)v);
  545. else {
  546. ACQUIRE_DTOA_LOCK(0);
  547. v->next = GET_STATE(freelist)[v->k];
  548. GET_STATE(freelist)[v->k] = v;
  549. FREE_DTOA_LOCK(0);
  550. }
  551. }
  552. }
  553. #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
  554. y->wds*sizeof(Long) + 2*sizeof(int))
  555. static Bigint *
  556. multadd
  557. #ifdef KR_headers
  558. (STATE_PARAM b, m, a) STATE_PARAM_DECL Bigint *b; int m, a;
  559. #else
  560. (STATE_PARAM Bigint *b, int m, int a) /* multiply by m and add a */
  561. #endif
  562. {
  563. int i, wds;
  564. #ifdef ULLong
  565. ULong *x;
  566. ULLong carry, y;
  567. #else
  568. ULong carry, *x, y;
  569. #ifdef Pack_32
  570. ULong xi, z;
  571. #endif
  572. #endif
  573. Bigint *b1;
  574. wds = b->wds;
  575. x = b->x;
  576. i = 0;
  577. carry = a;
  578. do {
  579. #ifdef ULLong
  580. y = *x * (ULLong)m + carry;
  581. carry = y >> 32;
  582. *x++ = (ULong) y & FFFFFFFF;
  583. #else
  584. #ifdef Pack_32
  585. xi = *x;
  586. y = (xi & 0xffff) * m + carry;
  587. z = (xi >> 16) * m + (y >> 16);
  588. carry = z >> 16;
  589. *x++ = (z << 16) + (y & 0xffff);
  590. #else
  591. y = *x * m + carry;
  592. carry = y >> 16;
  593. *x++ = y & 0xffff;
  594. #endif
  595. #endif
  596. }
  597. while(++i < wds);
  598. if (carry) {
  599. if (wds >= b->maxwds) {
  600. b1 = Balloc(PASS_STATE b->k+1);
  601. Bcopy(b1, b);
  602. Bfree(PASS_STATE b);
  603. b = b1;
  604. }
  605. b->x[wds++] = (ULong) carry;
  606. b->wds = wds;
  607. }
  608. return b;
  609. }
  610. static Bigint *
  611. s2b
  612. #ifdef KR_headers
  613. (STATE_PARAM s, nd0, nd, y9) STATE_PARAM_DECL CONST char *s; int nd0, nd; ULong y9;
  614. #else
  615. (STATE_PARAM CONST char *s, int nd0, int nd, ULong y9)
  616. #endif
  617. {
  618. Bigint *b;
  619. int i, k;
  620. Long x, y;
  621. x = (nd + 8) / 9;
  622. for(k = 0, y = 1; x > y; y <<= 1, k++) ;
  623. #ifdef Pack_32
  624. b = Balloc(PASS_STATE k);
  625. b->x[0] = y9;
  626. b->wds = 1;
  627. #else
  628. b = Balloc(PASS_STATE k+1);
  629. b->x[0] = y9 & 0xffff;
  630. b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
  631. #endif
  632. i = 9;
  633. if (9 < nd0) {
  634. s += 9;
  635. do b = multadd(PASS_STATE b, 10, *s++ - '0');
  636. while(++i < nd0);
  637. s++;
  638. }
  639. else
  640. s += 10;
  641. for(; i < nd; i++)
  642. b = multadd(PASS_STATE b, 10, *s++ - '0');
  643. return b;
  644. }
  645. static int
  646. hi0bits
  647. #ifdef KR_headers
  648. (x) register ULong x;
  649. #else
  650. (register ULong x)
  651. #endif
  652. {
  653. register int k = 0;
  654. if (!(x & 0xffff0000)) {
  655. k = 16;
  656. x <<= 16;
  657. }
  658. if (!(x & 0xff000000)) {
  659. k += 8;
  660. x <<= 8;
  661. }
  662. if (!(x & 0xf0000000)) {
  663. k += 4;
  664. x <<= 4;
  665. }
  666. if (!(x & 0xc0000000)) {
  667. k += 2;
  668. x <<= 2;
  669. }
  670. if (!(x & 0x80000000)) {
  671. k++;
  672. if (!(x & 0x40000000))
  673. return 32;
  674. }
  675. return k;
  676. }
  677. static int
  678. lo0bits
  679. #ifdef KR_headers
  680. (y) ULong *y;
  681. #else
  682. (ULong *y)
  683. #endif
  684. {
  685. register int k;
  686. register ULong x = *y;
  687. if (x & 7) {
  688. if (x & 1)
  689. return 0;
  690. if (x & 2) {
  691. *y = x >> 1;
  692. return 1;
  693. }
  694. *y = x >> 2;
  695. return 2;
  696. }
  697. k = 0;
  698. if (!(x & 0xffff)) {
  699. k = 16;
  700. x >>= 16;
  701. }
  702. if (!(x & 0xff)) {
  703. k += 8;
  704. x >>= 8;
  705. }
  706. if (!(x & 0xf)) {
  707. k += 4;
  708. x >>= 4;
  709. }
  710. if (!(x & 0x3)) {
  711. k += 2;
  712. x >>= 2;
  713. }
  714. if (!(x & 1)) {
  715. k++;
  716. x >>= 1;
  717. if (!x)
  718. return 32;
  719. }
  720. *y = x;
  721. return k;
  722. }
  723. static Bigint *
  724. i2b
  725. #ifdef KR_headers
  726. (STATE_PARAM i) STATE_PARAM_DECL int i;
  727. #else
  728. (STATE_PARAM int i)
  729. #endif
  730. {
  731. Bigint *b;
  732. b = Balloc(PASS_STATE 1);
  733. b->x[0] = i;
  734. b->wds = 1;
  735. return b;
  736. }
  737. static Bigint *
  738. mult
  739. #ifdef KR_headers
  740. (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
  741. #else
  742. (STATE_PARAM Bigint *a, Bigint *b)
  743. #endif
  744. {
  745. Bigint *c;
  746. int k, wa, wb, wc;
  747. ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
  748. ULong y;
  749. #ifdef ULLong
  750. ULLong carry, z;
  751. #else
  752. ULong carry, z;
  753. #ifdef Pack_32
  754. ULong z2;
  755. #endif
  756. #endif
  757. if (a->wds < b->wds) {
  758. c = a;
  759. a = b;
  760. b = c;
  761. }
  762. k = a->k;
  763. wa = a->wds;
  764. wb = b->wds;
  765. wc = wa + wb;
  766. if (wc > a->maxwds)
  767. k++;
  768. c = Balloc(PASS_STATE k);
  769. for(x = c->x, xa = x + wc; x < xa; x++)
  770. *x = 0;
  771. xa = a->x;
  772. xae = xa + wa;
  773. xb = b->x;
  774. xbe = xb + wb;
  775. xc0 = c->x;
  776. #ifdef ULLong
  777. for(; xb < xbe; xc0++) {
  778. if ((y = *xb++)) {
  779. x = xa;
  780. xc = xc0;
  781. carry = 0;
  782. do {
  783. z = *x++ * (ULLong)y + *xc + carry;
  784. carry = z >> 32;
  785. *xc++ = (ULong) z & FFFFFFFF;
  786. }
  787. while(x < xae);
  788. *xc = (ULong) carry;
  789. }
  790. }
  791. #else
  792. #ifdef Pack_32
  793. for(; xb < xbe; xb++, xc0++) {
  794. if (y = *xb & 0xffff) {
  795. x = xa;
  796. xc = xc0;
  797. carry = 0;
  798. do {
  799. z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
  800. carry = z >> 16;
  801. z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
  802. carry = z2 >> 16;
  803. Storeinc(xc, z2, z);
  804. }
  805. while(x < xae);
  806. *xc = carry;
  807. }
  808. if (y = *xb >> 16) {
  809. x = xa;
  810. xc = xc0;
  811. carry = 0;
  812. z2 = *xc;
  813. do {
  814. z = (*x & 0xffff) * y + (*xc >> 16) + carry;
  815. carry = z >> 16;
  816. Storeinc(xc, z, z2);
  817. z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
  818. carry = z2 >> 16;
  819. }
  820. while(x < xae);
  821. *xc = z2;
  822. }
  823. }
  824. #else
  825. for(; xb < xbe; xc0++) {
  826. if (y = *xb++) {
  827. x = xa;
  828. xc = xc0;
  829. carry = 0;
  830. do {
  831. z = *x++ * y + *xc + carry;
  832. carry = z >> 16;
  833. *xc++ = z & 0xffff;
  834. }
  835. while(x < xae);
  836. *xc = carry;
  837. }
  838. }
  839. #endif
  840. #endif
  841. for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
  842. c->wds = wc;
  843. return c;
  844. }
  845. static Bigint *
  846. pow5mult
  847. #ifdef KR_headers
  848. (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
  849. #else
  850. (STATE_PARAM Bigint *b, int k)
  851. #endif
  852. {
  853. Bigint *b1, *p5, *p51;
  854. int i;
  855. static CONST int p05[3] = { 5, 25, 125 };
  856. if ((i = k & 3))
  857. b = multadd(PASS_STATE b, p05[i-1], 0);
  858. if (!(k >>= 2))
  859. return b;
  860. if (!(p5 = GET_STATE(p5s))) {
  861. /* first time */
  862. #ifdef MULTIPLE_THREADS
  863. ACQUIRE_DTOA_LOCK(1);
  864. if (!(p5 = p5s)) {
  865. p5 = p5s = i2b(625);
  866. p5->next = 0;
  867. }
  868. FREE_DTOA_LOCK(1);
  869. #else
  870. p5 = GET_STATE(p5s) = i2b(PASS_STATE 625);
  871. p5->next = 0;
  872. #endif
  873. }
  874. for(;;) {
  875. if (k & 1) {
  876. b1 = mult(PASS_STATE b, p5);
  877. Bfree(PASS_STATE b);
  878. b = b1;
  879. }
  880. if (!(k >>= 1))
  881. break;
  882. if (!(p51 = p5->next)) {
  883. #ifdef MULTIPLE_THREADS
  884. ACQUIRE_DTOA_LOCK(1);
  885. if (!(p51 = p5->next)) {
  886. p51 = p5->next = mult(p5,p5);
  887. p51->next = 0;
  888. }
  889. FREE_DTOA_LOCK(1);
  890. #else
  891. p51 = p5->next = mult(PASS_STATE p5,p5);
  892. p51->next = 0;
  893. #endif
  894. }
  895. p5 = p51;
  896. }
  897. return b;
  898. }
  899. static Bigint *
  900. lshift
  901. #ifdef KR_headers
  902. (STATE_PARAM b, k) STATE_PARAM_DECL Bigint *b; int k;
  903. #else
  904. (STATE_PARAM Bigint *b, int k)
  905. #endif
  906. {
  907. int i, k1, n, n1;
  908. Bigint *b1;
  909. ULong *x, *x1, *xe, z;
  910. #ifdef Pack_32
  911. n = k >> 5;
  912. #else
  913. n = k >> 4;
  914. #endif
  915. k1 = b->k;
  916. n1 = n + b->wds + 1;
  917. for(i = b->maxwds; n1 > i; i <<= 1)
  918. k1++;
  919. b1 = Balloc(PASS_STATE k1);
  920. x1 = b1->x;
  921. for(i = 0; i < n; i++)
  922. *x1++ = 0;
  923. x = b->x;
  924. xe = x + b->wds;
  925. #ifdef Pack_32
  926. if (k &= 0x1f) {
  927. k1 = 32 - k;
  928. z = 0;
  929. do {
  930. *x1++ = *x << k | z;
  931. z = *x++ >> k1;
  932. }
  933. while(x < xe);
  934. if ((*x1 = z))
  935. ++n1;
  936. }
  937. #else
  938. if (k &= 0xf) {
  939. k1 = 16 - k;
  940. z = 0;
  941. do {
  942. *x1++ = *x << k & 0xffff | z;
  943. z = *x++ >> k1;
  944. }
  945. while(x < xe);
  946. if (*x1 = z)
  947. ++n1;
  948. }
  949. #endif
  950. else do
  951. *x1++ = *x++;
  952. while(x < xe);
  953. b1->wds = n1 - 1;
  954. Bfree(PASS_STATE b);
  955. return b1;
  956. }
  957. static int
  958. cmp
  959. #ifdef KR_headers
  960. (a, b) Bigint *a, *b;
  961. #else
  962. (Bigint *a, Bigint *b)
  963. #endif
  964. {
  965. ULong *xa, *xa0, *xb, *xb0;
  966. int i, j;
  967. i = a->wds;
  968. j = b->wds;
  969. #ifdef DEBUG
  970. if (i > 1 && !a->x[i-1])
  971. Bug("cmp called with a->x[a->wds-1] == 0");
  972. if (j > 1 && !b->x[j-1])
  973. Bug("cmp called with b->x[b->wds-1] == 0");
  974. #endif
  975. if (i -= j)
  976. return i;
  977. xa0 = a->x;
  978. xa = xa0 + j;
  979. xb0 = b->x;
  980. xb = xb0 + j;
  981. for(;;) {
  982. if (*--xa != *--xb)
  983. return *xa < *xb ? -1 : 1;
  984. if (xa <= xa0)
  985. break;
  986. }
  987. return 0;
  988. }
  989. static Bigint *
  990. diff
  991. #ifdef KR_headers
  992. (STATE_PARAM a, b) STATE_PARAM_DECL Bigint *a, *b;
  993. #else
  994. (STATE_PARAM Bigint *a, Bigint *b)
  995. #endif
  996. {
  997. Bigint *c;
  998. int i, wa, wb;
  999. ULong *xa, *xae, *xb, *xbe, *xc;
  1000. #ifdef ULLong
  1001. ULLong borrow, y;
  1002. #else
  1003. ULong borrow, y;
  1004. #ifdef Pack_32
  1005. ULong z;
  1006. #endif
  1007. #endif
  1008. i = cmp(a,b);
  1009. if (!i) {
  1010. c = Balloc(PASS_STATE 0);
  1011. c->wds = 1;
  1012. c->x[0] = 0;
  1013. return c;
  1014. }
  1015. if (i < 0) {
  1016. c = a;
  1017. a = b;
  1018. b = c;
  1019. i = 1;
  1020. }
  1021. else
  1022. i = 0;
  1023. c = Balloc(PASS_STATE a->k);
  1024. c->sign = i;
  1025. wa = a->wds;
  1026. xa = a->x;
  1027. xae = xa + wa;
  1028. wb = b->wds;
  1029. xb = b->x;
  1030. xbe = xb + wb;
  1031. xc = c->x;
  1032. borrow = 0;
  1033. #ifdef ULLong
  1034. do {
  1035. y = (ULLong)*xa++ - *xb++ - borrow;
  1036. borrow = y >> 32 & (ULong)1;
  1037. *xc++ = (ULong) y & FFFFFFFF;
  1038. }
  1039. while(xb < xbe);
  1040. while(xa < xae) {
  1041. y = *xa++ - borrow;
  1042. borrow = y >> 32 & (ULong)1;
  1043. *xc++ = (ULong) y & FFFFFFFF;
  1044. }
  1045. #else
  1046. #ifdef Pack_32
  1047. do {
  1048. y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
  1049. borrow = (y & 0x10000) >> 16;
  1050. z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
  1051. borrow = (z & 0x10000) >> 16;
  1052. Storeinc(xc, z, y);
  1053. }
  1054. while(xb < xbe);
  1055. while(xa < xae) {
  1056. y = (*xa & 0xffff) - borrow;
  1057. borrow = (y & 0x10000) >> 16;
  1058. z = (*xa++ >> 16) - borrow;
  1059. borrow = (z & 0x10000) >> 16;
  1060. Storeinc(xc, z, y);
  1061. }
  1062. #else
  1063. do {
  1064. y = *xa++ - *xb++ - borrow;
  1065. borrow = (y & 0x10000) >> 16;
  1066. *xc++ = y & 0xffff;
  1067. }
  1068. while(xb < xbe);
  1069. while(xa < xae) {
  1070. y = *xa++ - borrow;
  1071. borrow = (y & 0x10000) >> 16;
  1072. *xc++ = y & 0xffff;
  1073. }
  1074. #endif
  1075. #endif
  1076. while(!*--xc)
  1077. wa--;
  1078. c->wds = wa;
  1079. return c;
  1080. }
  1081. static double
  1082. ulp
  1083. #ifdef KR_headers
  1084. (x) U x;
  1085. #else
  1086. (U x)
  1087. #endif
  1088. {
  1089. register Long L;
  1090. U a;
  1091. L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
  1092. #ifndef Avoid_Underflow
  1093. #ifndef Sudden_Underflow
  1094. if (L > 0) {
  1095. #endif
  1096. #endif
  1097. #ifdef IBM
  1098. L |= Exp_msk1 >> 4;
  1099. #endif
  1100. word0(a) = L;
  1101. word1(a) = 0;
  1102. #ifndef Avoid_Underflow
  1103. #ifndef Sudden_Underflow
  1104. }
  1105. else {
  1106. L = -L >> Exp_shift;
  1107. if (L < Exp_shift) {
  1108. word0(a) = 0x80000 >> L;
  1109. word1(a) = 0;
  1110. }
  1111. else {
  1112. word0(a) = 0;
  1113. L -= Exp_shift;
  1114. word1(a) = L >= 31 ? 1 : 1 << 31 - L;
  1115. }
  1116. }
  1117. #endif
  1118. #endif
  1119. return dval(a);
  1120. }
  1121. static double
  1122. b2d
  1123. #ifdef KR_headers
  1124. (a, e) Bigint *a; int *e;
  1125. #else
  1126. (Bigint *a, int *e)
  1127. #endif
  1128. {
  1129. ULong *xa, *xa0, w, y, z;
  1130. int k;
  1131. U d;
  1132. #ifdef VAX
  1133. ULong d0, d1;
  1134. #else
  1135. #define d0 word0(d)
  1136. #define d1 word1(d)
  1137. #endif
  1138. xa0 = a->x;
  1139. xa = xa0 + a->wds;
  1140. y = *--xa;
  1141. #ifdef DEBUG
  1142. if (!y) Bug("zero y in b2d");
  1143. #endif
  1144. k = hi0bits(y);
  1145. *e = 32 - k;
  1146. #ifdef Pack_32
  1147. if (k < Ebits) {
  1148. d0 = Exp_1 | y >> (Ebits - k);
  1149. w = xa > xa0 ? *--xa : 0;
  1150. d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
  1151. goto ret_d;
  1152. }
  1153. z = xa > xa0 ? *--xa : 0;
  1154. if (k -= Ebits) {
  1155. d0 = Exp_1 | y << k | z >> (32 - k);
  1156. y = xa > xa0 ? *--xa : 0;
  1157. d1 = z << k | y >> (32 - k);
  1158. }
  1159. else {
  1160. d0 = Exp_1 | y;
  1161. d1 = z;
  1162. }
  1163. #else
  1164. if (k < Ebits + 16) {
  1165. z = xa > xa0 ? *--xa : 0;
  1166. d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
  1167. w = xa > xa0 ? *--xa : 0;
  1168. y = xa > xa0 ? *--xa : 0;
  1169. d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
  1170. goto ret_d;
  1171. }
  1172. z = xa > xa0 ? *--xa : 0;
  1173. w = xa > xa0 ? *--xa : 0;
  1174. k -= Ebits + 16;
  1175. d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
  1176. y = xa > xa0 ? *--xa : 0;
  1177. d1 = w << k + 16 | y << k;
  1178. #endif
  1179. ret_d:
  1180. #ifdef VAX
  1181. word0(d) = d0 >> 16 | d0 << 16;
  1182. word1(d) = d1 >> 16 | d1 << 16;
  1183. #else
  1184. #undef d0
  1185. #undef d1
  1186. #endif
  1187. return dval(d);
  1188. }
  1189. static Bigint *
  1190. d2b
  1191. #ifdef KR_headers
  1192. (STATE_PARAM d, e, bits) STATE_PARAM_DECL U d; int *e, *bits;
  1193. #else
  1194. (STATE_PARAM U d, int *e, int *bits)
  1195. #endif
  1196. {
  1197. Bigint *b;
  1198. int de, k;
  1199. ULong *x, y, z;
  1200. #ifndef Sudden_Underflow
  1201. int i;
  1202. #endif
  1203. #ifdef VAX
  1204. ULong d0, d1;
  1205. d0 = word0(d) >> 16 | word0(d) << 16;
  1206. d1 = word1(d) >> 16 | word1(d) << 16;
  1207. #else
  1208. #define d0 word0(d)
  1209. #define d1 word1(d)
  1210. #endif
  1211. #ifdef Pack_32
  1212. b = Balloc(PASS_STATE 1);
  1213. #else
  1214. b = Balloc(PASS_STATE 2);
  1215. #endif
  1216. x = b->x;
  1217. z = d0 & Frac_mask;
  1218. d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
  1219. #ifdef Sudden_Underflow
  1220. de = (int)(d0 >> Exp_shift);
  1221. #ifndef IBM
  1222. z |= Exp_msk11;
  1223. #endif
  1224. #else
  1225. if ((de = (int)(d0 >> Exp_shift)))
  1226. z |= Exp_msk1;
  1227. #endif
  1228. #ifdef Pack_32
  1229. if ((y = d1)) {
  1230. if ((k = lo0bits(&y))) {
  1231. x[0] = y | z << (32 - k);
  1232. z >>= k;
  1233. }
  1234. else
  1235. x[0] = y;
  1236. #ifndef Sudden_Underflow
  1237. i =
  1238. #endif
  1239. b->wds = (x[1] = z) ? 2 : 1;
  1240. }
  1241. else {
  1242. k = lo0bits(&z);
  1243. x[0] = z;
  1244. #ifndef Sudden_Underflow
  1245. i =
  1246. #endif
  1247. b->wds = 1;
  1248. k += 32;
  1249. }
  1250. #else
  1251. if (y = d1) {
  1252. if (k = lo0bits(&y))
  1253. if (k >= 16) {
  1254. x[0] = y | z << 32 - k & 0xffff;
  1255. x[1] = z >> k - 16 & 0xffff;
  1256. x[2] = z >> k;
  1257. i = 2;
  1258. }
  1259. else {
  1260. x[0] = y & 0xffff;
  1261. x[1] = y >> 16 | z << 16 - k & 0xffff;
  1262. x[2] = z >> k & 0xffff;
  1263. x[3] = z >> k+16;
  1264. i = 3;
  1265. }
  1266. else {
  1267. x[0] = y & 0xffff;
  1268. x[1] = y >> 16;
  1269. x[2] = z & 0xffff;
  1270. x[3] = z >> 16;
  1271. i = 3;
  1272. }
  1273. }
  1274. else {
  1275. #ifdef DEBUG
  1276. if (!z)
  1277. Bug("Zero passed to d2b");
  1278. #endif
  1279. k = lo0bits(&z);
  1280. if (k >= 16) {
  1281. x[0] = z;
  1282. i = 0;
  1283. }
  1284. else {
  1285. x[0] = z & 0xffff;
  1286. x[1] = z >> 16;
  1287. i = 1;
  1288. }
  1289. k += 32;
  1290. }
  1291. while(!x[i])
  1292. --i;
  1293. b->wds = i + 1;
  1294. #endif
  1295. #ifndef Sudden_Underflow
  1296. if (de) {
  1297. #endif
  1298. #ifdef IBM
  1299. *e = (de - Bias - (P-1) << 2) + k;
  1300. *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
  1301. #else
  1302. *e = de - Bias - (P-1) + k;
  1303. *bits = P - k;
  1304. #endif
  1305. #ifndef Sudden_Underflow
  1306. }
  1307. else {
  1308. *e = de - Bias - (P-1) + 1 + k;
  1309. #ifdef Pack_32
  1310. *bits = 32*i - hi0bits(x[i-1]);
  1311. #else
  1312. *bits = (i+2)*16 - hi0bits(x[i]);
  1313. #endif
  1314. }
  1315. #endif
  1316. return b;
  1317. }
  1318. #undef d0
  1319. #undef d1
  1320. static double
  1321. ratio
  1322. #ifdef KR_headers
  1323. (a, b) Bigint *a, *b;
  1324. #else
  1325. (Bigint *a, Bigint *b)
  1326. #endif
  1327. {
  1328. U da, db;
  1329. int k, ka, kb;
  1330. dval(da) = b2d(a, &ka);
  1331. dval(db) = b2d(b, &kb);
  1332. #ifdef Pack_32
  1333. k = ka - kb + 32*(a->wds - b->wds);
  1334. #else
  1335. k = ka - kb + 16*(a->wds - b->wds);
  1336. #endif
  1337. #ifdef IBM
  1338. if (k > 0) {
  1339. word0(da) += (k >> 2)*Exp_msk1;
  1340. if (k &= 3)
  1341. dval(da) *= 1 << k;
  1342. }
  1343. else {
  1344. k = -k;
  1345. word0(db) += (k >> 2)*Exp_msk1;
  1346. if (k &= 3)
  1347. dval(db) *= 1 << k;
  1348. }
  1349. #else
  1350. if (k > 0)
  1351. word0(da) += k*Exp_msk1;
  1352. else {
  1353. k = -k;
  1354. word0(db) += k*Exp_msk1;
  1355. }
  1356. #endif
  1357. return dval(da) / dval(db);
  1358. }
  1359. static CONST double
  1360. tens[] = {
  1361. 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
  1362. 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
  1363. 1e20, 1e21, 1e22
  1364. #ifdef VAX
  1365. , 1e23, 1e24
  1366. #endif
  1367. };
  1368. static CONST double
  1369. #ifdef IEEE_Arith
  1370. bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
  1371. static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
  1372. #ifdef Avoid_Underflow
  1373. 9007199254740992.*9007199254740992.e-256
  1374. /* = 2^106 * 1e-53 */
  1375. #else
  1376. 1e-256
  1377. #endif
  1378. };
  1379. /* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
  1380. /* flag unnecessarily. It leads to a song and dance at the end of strtod. */
  1381. #define Scale_Bit 0x10
  1382. #define n_bigtens 5
  1383. #else
  1384. #ifdef IBM
  1385. bigtens[] = { 1e16, 1e32, 1e64 };
  1386. static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
  1387. #define n_bigtens 3
  1388. #else
  1389. bigtens[] = { 1e16, 1e32 };
  1390. static CONST double tinytens[] = { 1e-16, 1e-32 };
  1391. #define n_bigtens 2
  1392. #endif
  1393. #endif
  1394. static double
  1395. _strtod
  1396. #ifdef KR_headers
  1397. (STATE_PARAM s00, se) STATE_PARAM_DECL CONST char *s00; char **se;
  1398. #else
  1399. (STATE_PARAM CONST char *s00, char **se)
  1400. #endif
  1401. {
  1402. #ifdef Avoid_Underflow
  1403. int scale;
  1404. #endif
  1405. int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign,
  1406. e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
  1407. CONST char *s, *s0, *s1;
  1408. double aadj, adj;
  1409. U aadj1, rv, rv0;
  1410. Long L;
  1411. ULong y, z;
  1412. Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
  1413. #ifdef SET_INEXACT
  1414. int inexact, oldinexact;
  1415. #endif
  1416. #ifdef Honor_FLT_ROUNDS
  1417. int rounding;
  1418. #endif
  1419. #ifdef USE_LOCALE
  1420. CONST char *s2;
  1421. #endif
  1422. #ifdef __GNUC__
  1423. delta = bb = bd = bs = 0;
  1424. #endif
  1425. sign = nz0 = nz = 0;
  1426. dval(rv) = 0.;
  1427. for(s = s00;;s++) switch(*s) {
  1428. case '-':
  1429. sign = 1;
  1430. /* no break */
  1431. case '+':
  1432. if (*++s)
  1433. goto break2;
  1434. /* no break */
  1435. case 0:
  1436. goto ret0;
  1437. case '\t':
  1438. case '\n':
  1439. case '\v':
  1440. case '\f':
  1441. case '\r':
  1442. case ' ':
  1443. continue;
  1444. default:
  1445. goto break2;
  1446. }
  1447. break2:
  1448. if (*s == '0') {
  1449. nz0 = 1;
  1450. while(*++s == '0') ;
  1451. if (!*s)
  1452. goto ret;
  1453. }
  1454. s0 = s;
  1455. y = z = 0;
  1456. for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
  1457. if (nd < 9)
  1458. y = 10*y + c - '0';
  1459. else if (nd < 16)
  1460. z = 10*z + c - '0';
  1461. nd0 = nd;
  1462. #ifdef USE_LOCALE
  1463. s1 = localeconv()->decimal_point;
  1464. if (c == *s1) {
  1465. c = '.';
  1466. if (*++s1) {
  1467. s2 = s;
  1468. for(;;) {
  1469. if (*++s2 != *s1) {
  1470. c = 0;
  1471. break;
  1472. }
  1473. if (!*++s1) {
  1474. s = s2;
  1475. break;
  1476. }
  1477. }
  1478. }
  1479. }
  1480. #endif
  1481. if (c == '.') {
  1482. c = *++s;
  1483. if (!nd) {
  1484. for(; c == '0'; c = *++s)
  1485. nz++;
  1486. if (c > '0' && c <= '9') {
  1487. s0 = s;
  1488. nf += nz;
  1489. nz = 0;
  1490. goto have_dig;
  1491. }
  1492. goto dig_done;
  1493. }
  1494. for(; c >= '0' && c <= '9'; c = *++s) {
  1495. have_dig:
  1496. nz++;
  1497. if (c -= '0') {
  1498. nf += nz;
  1499. for(i = 1; i < nz; i++)
  1500. if (nd++ < 9)
  1501. y *= 10;
  1502. else if (nd <= DBL_DIG + 1)
  1503. z *= 10;
  1504. if (nd++ < 9)
  1505. y = 10*y + c;
  1506. else if (nd <= DBL_DIG + 1)
  1507. z = 10*z + c;
  1508. nz = 0;
  1509. }
  1510. }
  1511. }
  1512. dig_done:
  1513. e = 0;
  1514. if (c == 'e' || c == 'E') {
  1515. if (!nd && !nz && !nz0) {
  1516. goto ret0;
  1517. }
  1518. s00 = s;
  1519. esign = 0;
  1520. switch(c = *++s) {
  1521. case '-':
  1522. esign = 1;
  1523. case '+':
  1524. c = *++s;
  1525. }
  1526. if (c >= '0' && c <= '9') {
  1527. while(c == '0')
  1528. c = *++s;
  1529. if (c > '0' && c <= '9') {
  1530. L = c - '0';
  1531. s1 = s;
  1532. while((c = *++s) >= '0' && c <= '9')
  1533. L = 10*L + c - '0';
  1534. if (s - s1 > 8 || L > 19999)
  1535. /* Avoid confusion from exponents
  1536. * so large that e might overflow.
  1537. */
  1538. e = 19999; /* safe for 16 bit ints */
  1539. else
  1540. e = (int)L;
  1541. if (esign)
  1542. e = -e;
  1543. }
  1544. else
  1545. e = 0;
  1546. }
  1547. else
  1548. s = s00;
  1549. }
  1550. if (!nd) {
  1551. if (!nz && !nz0) {
  1552. ret0:
  1553. s = s00;
  1554. sign = 0;
  1555. }
  1556. goto ret;
  1557. }
  1558. e1 = e -= nf;
  1559. /* Now we have nd0 digits, starting at s0, followed by a
  1560. * decimal point, followed by nd-nd0 digits. The number we're
  1561. * after is the integer represented by those digits times
  1562. * 10**e */
  1563. if (!nd0)
  1564. nd0 = nd;
  1565. k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
  1566. dval(rv) = y;
  1567. if (k > 9) {
  1568. #ifdef SET_INEXACT
  1569. if (k > DBL_DIG)
  1570. oldinexact = get_inexact();
  1571. #endif
  1572. dval(rv) = tens[k - 9] * dval(rv) + z;
  1573. }
  1574. bd0 = 0;
  1575. if (nd <= DBL_DIG
  1576. #ifndef RND_PRODQUOT
  1577. #ifndef Honor_FLT_ROUNDS
  1578. && Flt_Rounds == 1
  1579. #endif
  1580. #endif
  1581. ) {
  1582. if (!e)
  1583. goto ret;
  1584. if (e > 0) {
  1585. if (e <= Ten_pmax) {
  1586. #ifdef VAX
  1587. goto vax_ovfl_check;
  1588. #else
  1589. #ifdef Honor_FLT_ROUNDS
  1590. /* round correctly FLT_ROUNDS = 2 or 3 */
  1591. if (sign) {
  1592. rv = -rv;
  1593. sign = 0;
  1594. }
  1595. #endif
  1596. /* rv = */ rounded_product(dval(rv), tens[e]);
  1597. goto ret;
  1598. #endif
  1599. }
  1600. i = DBL_DIG - nd;
  1601. if (e <= Ten_pmax + i) {
  1602. /* A fancier test would sometimes let us do
  1603. * this for larger i values.
  1604. */
  1605. #ifdef Honor_FLT_ROUNDS
  1606. /* round correctly FLT_ROUNDS = 2 or 3 */
  1607. if (sign) {
  1608. rv = -rv;
  1609. sign = 0;
  1610. }
  1611. #endif
  1612. e -= i;
  1613. dval(rv) *= tens[i];
  1614. #ifdef VAX
  1615. /* VAX exponent range is so narrow we must
  1616. * worry about overflow here...
  1617. */
  1618. vax_ovfl_check:
  1619. word0(rv) -= P*Exp_msk1;
  1620. /* rv = */ rounded_product(dval(rv), tens[e]);
  1621. if ((word0(rv) & Exp_mask)
  1622. > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
  1623. goto ovfl;
  1624. word0(rv) += P*Exp_msk1;
  1625. #else
  1626. /* rv = */ rounded_product(dval(rv), tens[e]);
  1627. #endif
  1628. goto ret;
  1629. }
  1630. }
  1631. #ifndef Inaccurate_Divide
  1632. else if (e >= -Ten_pmax) {
  1633. #ifdef Honor_FLT_ROUNDS
  1634. /* round correctly FLT_ROUNDS = 2 or 3 */
  1635. if (sign) {
  1636. rv = -rv;
  1637. sign = 0;
  1638. }
  1639. #endif
  1640. /* rv = */ rounded_quotient(dval(rv), tens[-e]);
  1641. goto ret;
  1642. }
  1643. #endif
  1644. }
  1645. e1 += nd - k;
  1646. #ifdef IEEE_Arith
  1647. #ifdef SET_INEXACT
  1648. inexact = 1;
  1649. if (k <= DBL_DIG)
  1650. oldinexact = get_inexact();
  1651. #endif
  1652. #ifdef Avoid_Underflow
  1653. scale = 0;
  1654. #endif
  1655. #ifdef Honor_FLT_ROUNDS
  1656. if ((rounding = Flt_Rounds) >= 2) {
  1657. if (sign)
  1658. rounding = rounding == 2 ? 0 : 2;
  1659. else
  1660. if (rounding != 2)
  1661. rounding = 0;
  1662. }
  1663. #endif
  1664. #endif /*IEEE_Arith*/
  1665. /* Get starting approximation = rv * 10**e1 */
  1666. if (e1 > 0) {
  1667. if ((i = e1 & 15))
  1668. dval(rv) *= tens[i];
  1669. if (e1 &= ~15) {
  1670. if (e1 > DBL_MAX_10_EXP) {
  1671. ovfl:
  1672. #ifndef NO_ERRNO
  1673. errno = ERANGE;
  1674. #endif
  1675. /* Can't trust HUGE_VAL */
  1676. #ifdef IEEE_Arith
  1677. #ifdef Honor_FLT_ROUNDS
  1678. switch(rounding) {
  1679. case 0: /* toward 0 */
  1680. case 3: /* toward -infinity */
  1681. word0(rv) = Big0;
  1682. word1(rv) = Big1;
  1683. break;
  1684. default:
  1685. word0(rv) = Exp_mask;
  1686. word1(rv) = 0;
  1687. }
  1688. #else /*Honor_FLT_ROUNDS*/
  1689. word0(rv) = Exp_mask;
  1690. word1(rv) = 0;
  1691. #endif /*Honor_FLT_ROUNDS*/
  1692. #ifdef SET_INEXACT
  1693. /* set overflow bit */
  1694. dval(rv0) = 1e300;
  1695. dval(rv0) *= dval(rv0);
  1696. #endif
  1697. #else /*IEEE_Arith*/
  1698. word0(rv) = Big0;
  1699. word1(rv) = Big1;
  1700. #endif /*IEEE_Arith*/
  1701. if (bd0)
  1702. goto retfree;
  1703. goto ret;
  1704. }
  1705. e1 >>= 4;
  1706. for(j = 0; e1 > 1; j++, e1 >>= 1)
  1707. if (e1 & 1)
  1708. dval(rv) *= bigtens[j];
  1709. /* The last multiplication could overflow. */
  1710. word0(rv) -= P*Exp_msk1;
  1711. dval(rv) *= bigtens[j];
  1712. if ((z = word0(rv) & Exp_mask)
  1713. > Exp_msk1*(DBL_MAX_EXP+Bias-P))
  1714. goto ovfl;
  1715. if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
  1716. /* set to largest number */
  1717. /* (Can't trust DBL_MAX) */
  1718. word0(rv) = Big0;
  1719. word1(rv) = Big1;
  1720. }
  1721. else
  1722. word0(rv) += P*Exp_msk1;
  1723. }
  1724. }
  1725. else if (e1 < 0) {
  1726. e1 = -e1;
  1727. if ((i = e1 & 15))
  1728. dval(rv) /= tens[i];
  1729. if (e1 >>= 4) {
  1730. if (e1 >= 1 << n_bigtens)
  1731. goto undfl;
  1732. #ifdef Avoid_Underflow
  1733. if (e1 & Scale_Bit)
  1734. scale = 2*P;
  1735. for(j = 0; e1 > 0; j++, e1 >>= 1)
  1736. if (e1 & 1)
  1737. dval(rv) *= tinytens[j];
  1738. if (scale && (j = 2*P + 1 - ((word0(rv) & Exp_mask)
  1739. >> Exp_shift)) > 0) {
  1740. /* scaled rv is denormal; zap j low bits */
  1741. if (j >= 32) {
  1742. word1(rv) = 0;
  1743. if (j >= 53)
  1744. word0(rv) = (P+2)*Exp_msk1;
  1745. else
  1746. word0(rv) &= 0xffffffff << (j-32);
  1747. }
  1748. else
  1749. word1(rv) &= 0xffffffff << j;
  1750. }
  1751. #else
  1752. for(j = 0; e1 > 1; j++, e1 >>= 1)
  1753. if (e1 & 1)
  1754. dval(rv) *= tinytens[j];
  1755. /* The last multiplication could underflow. */
  1756. dval(rv0) = dval(rv);
  1757. dval(rv) *= tinytens[j];
  1758. if (!dval(rv)) {
  1759. dval(rv) = 2.*dval(rv0);
  1760. dval(rv) *= tinytens[j];
  1761. #endif
  1762. if (!dval(rv)) {
  1763. undfl:
  1764. dval(rv) = 0.;
  1765. #ifndef NO_ERRNO
  1766. errno = ERANGE;
  1767. #endif
  1768. if (bd0)
  1769. goto retfree;
  1770. goto ret;
  1771. }
  1772. #ifndef Avoid_Underflow
  1773. word0(rv) = Tiny0;
  1774. word1(rv) = Tiny1;
  1775. /* The refinement below will clean
  1776. * this approximation up.
  1777. */
  1778. }
  1779. #endif
  1780. }
  1781. }
  1782. /* Now the hard part -- adjusting rv to the correct value.*/
  1783. /* Put digits into bd: true value = bd * 10^e */
  1784. bd0 = s2b(PASS_STATE s0, nd0, nd, y);
  1785. for(;;) {
  1786. bd = Balloc(PASS_STATE bd0->k);
  1787. Bcopy(bd, bd0);
  1788. bb = d2b(PASS_STATE rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
  1789. bs = i2b(PASS_STATE 1);
  1790. if (e >= 0) {
  1791. bb2 = bb5 = 0;
  1792. bd2 = bd5 = e;
  1793. }
  1794. else {
  1795. bb2 = bb5 = -e;
  1796. bd2 = bd5 = 0;
  1797. }
  1798. if (bbe >= 0)
  1799. bb2 += bbe;
  1800. else
  1801. bd2 -= bbe;
  1802. bs2 = bb2;
  1803. #ifdef Honor_FLT_ROUNDS
  1804. if (rounding != 1)
  1805. bs2++;
  1806. #endif
  1807. #ifdef Avoid_Underflow
  1808. j = bbe - scale;
  1809. i = j + bbbits - 1; /* logb(rv) */
  1810. if (i < Emin) /* denormal */
  1811. j += P - Emin;
  1812. else
  1813. j = P + 1 - bbbits;
  1814. #else /*Avoid_Underflow*/
  1815. #ifdef Sudden_Underflow
  1816. #ifdef IBM
  1817. j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
  1818. #else
  1819. j = P + 1 - bbbits;
  1820. #endif
  1821. #else /*Sudden_Underflow*/
  1822. j = bbe;
  1823. i = j + bbbits - 1; /* logb(rv) */
  1824. if (i < Emin) /* denormal */
  1825. j += P - Emin;
  1826. else
  1827. j = P + 1 - bbbits;
  1828. #endif /*Sudden_Underflow*/
  1829. #endif /*Avoid_Underflow*/
  1830. bb2 += j;
  1831. bd2 += j;
  1832. #ifdef Avoid_Underflow
  1833. bd2 += scale;
  1834. #endif
  1835. i = bb2 < bd2 ? bb2 : bd2;
  1836. if (i > bs2)
  1837. i = bs2;
  1838. if (i > 0) {
  1839. bb2 -= i;
  1840. bd2 -= i;
  1841. bs2 -= i;
  1842. }
  1843. if (bb5 > 0) {
  1844. bs = pow5mult(PASS_STATE bs, bb5);
  1845. bb1 = mult(PASS_STATE bs, bb);
  1846. Bfree(PASS_STATE bb);
  1847. bb = bb1;
  1848. }
  1849. if (bb2 > 0)
  1850. bb = lshift(PASS_STATE bb, bb2);
  1851. if (bd5 > 0)
  1852. bd = pow5mult(PASS_STATE bd, bd5);
  1853. if (bd2 > 0)
  1854. bd = lshift(PASS_STATE bd, bd2);
  1855. if (bs2 > 0)
  1856. bs = lshift(PASS_STATE bs, bs2);
  1857. delta = diff(PASS_STATE bb, bd);
  1858. dsign = delta->sign;
  1859. delta->sign = 0;
  1860. i = cmp(delta, bs);
  1861. #ifdef Honor_FLT_ROUNDS
  1862. if (rounding != 1) {
  1863. if (i < 0) {
  1864. /* Error is less than an ulp */
  1865. if (!delta->x[0] && delta->wds <= 1) {
  1866. /* exact */
  1867. #ifdef SET_INEXACT
  1868. inexact = 0;
  1869. #endif
  1870. break;
  1871. }
  1872. if (rounding) {
  1873. if (dsign) {
  1874. adj = 1.;
  1875. goto apply_adj;
  1876. }
  1877. }
  1878. else if (!dsign) {
  1879. adj = -1.;
  1880. if (!word1(rv)
  1881. && !(word0(rv) & Frac_mask)) {
  1882. y = word0(rv) & Exp_mask;
  1883. #ifdef Avoid_Underflow
  1884. if (!scale || y > 2*P*Exp_msk1)
  1885. #else
  1886. if (y)
  1887. #endif
  1888. {
  1889. delta = lshift(PASS_STATE delta,Log2P);
  1890. if (cmp(delta, bs) <= 0)
  1891. adj = -0.5;
  1892. }
  1893. }
  1894. apply_adj:
  1895. #ifdef Avoid_Underflow
  1896. if (scale && (y = word0(rv) & Exp_mask)
  1897. <= 2*P*Exp_msk1)
  1898. word0(adj) += (2*P+1)*Exp_msk1 - y;
  1899. #else
  1900. #ifdef Sudden_Underflow
  1901. if ((word0(rv) & Exp_mask) <=
  1902. P*Exp_msk1) {
  1903. word0(rv) += P*Exp_msk1;
  1904. dval(rv) += adj*ulp(rv);
  1905. word0(rv) -= P*Exp_msk1;
  1906. }
  1907. else
  1908. #endif /*Sudden_Underflow*/
  1909. #endif /*Avoid_Underflow*/
  1910. dval(rv) += adj*ulp(rv);
  1911. }
  1912. break;
  1913. }
  1914. adj = ratio(delta, bs);
  1915. if (adj < 1.)
  1916. adj = 1.;
  1917. if (adj <= 0x7ffffffe) {
  1918. /* adj = rounding ? ceil(adj) : floor(adj); */
  1919. y = adj;
  1920. if (y != adj) {
  1921. if (!((rounding>>1) ^ dsign))
  1922. y++;
  1923. adj = y;
  1924. }
  1925. }
  1926. #ifdef Avoid_Underflow
  1927. if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
  1928. word0(adj) += (2*P+1)*Exp_msk1 - y;
  1929. #else
  1930. #ifdef Sudden_Underflow
  1931. if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
  1932. word0(rv) += P*Exp_msk1;
  1933. adj *= ulp(rv);
  1934. if (dsign)
  1935. dval(rv) += adj;
  1936. else
  1937. dval(rv) -= adj;
  1938. word0(rv) -= P*Exp_msk1;
  1939. goto cont;
  1940. }
  1941. #endif /*Sudden_Underflow*/
  1942. #endif /*Avoid_Underflow*/
  1943. adj *= ulp(rv);
  1944. if (dsign)
  1945. dval(rv) += adj;
  1946. else
  1947. dval(rv) -= adj;
  1948. goto cont;
  1949. }
  1950. #endif /*Honor_FLT_ROUNDS*/
  1951. if (i < 0) {
  1952. /* Error is less than half an ulp -- check for
  1953. * special case of mantissa a power of two.
  1954. */
  1955. if (dsign || word1(rv) || word0(rv) & Bndry_mask
  1956. #ifdef IEEE_Arith
  1957. #ifdef Avoid_Underflow
  1958. || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1
  1959. #else
  1960. || (word0(rv) & Exp_mask) <= Exp_msk1
  1961. #endif
  1962. #endif
  1963. ) {
  1964. #ifdef SET_INEXACT
  1965. if (!delta->x[0] && delta->wds <= 1)
  1966. inexact = 0;
  1967. #endif
  1968. break;
  1969. }
  1970. if (!delta->x[0] && delta->wds <= 1) {
  1971. /* exact result */
  1972. #ifdef SET_INEXACT
  1973. inexact = 0;
  1974. #endif
  1975. break;
  1976. }
  1977. delta = lshift(PASS_STATE delta,Log2P);
  1978. if (cmp(delta, bs) > 0)
  1979. goto drop_down;
  1980. break;
  1981. }
  1982. if (i == 0) {
  1983. /* exactly half-way between */
  1984. if (dsign) {
  1985. if ((word0(rv) & Bndry_mask1) == Bndry_mask1
  1986. && word1(rv) == (
  1987. #ifdef Avoid_Underflow
  1988. (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1)
  1989. ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
  1990. #endif
  1991. 0xffffffff)) {
  1992. /*boundary case -- increment exponent*/
  1993. word0(rv) = (word0(rv) & Exp_mask)
  1994. + Exp_msk1
  1995. #ifdef IBM
  1996. | Exp_msk1 >> 4
  1997. #endif
  1998. ;
  1999. word1(rv) = 0;
  2000. #ifdef Avoid_Underflow
  2001. dsign = 0;
  2002. #endif
  2003. break;
  2004. }
  2005. }
  2006. else if (!(word0(rv) & Bndry_mask) && !word1(rv)) {
  2007. drop_down:
  2008. /* boundary case -- decrement exponent */
  2009. #ifdef Sudden_Underflow /*{{*/
  2010. L = word0(rv) & Exp_mask;
  2011. #ifdef IBM
  2012. if (L < Exp_msk1)
  2013. #else
  2014. #ifdef Avoid_Underflow
  2015. if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
  2016. #else
  2017. if (L <= Exp_msk1)
  2018. #endif /*Avoid_Underflow*/
  2019. #endif /*IBM*/
  2020. goto undfl;
  2021. L -= Exp_msk1;
  2022. #else /*Sudden_Underflow}{*/
  2023. #ifdef Avoid_Underflow
  2024. if (scale) {
  2025. L = word0(rv) & Exp_mask;
  2026. if (L <= (2*P+1)*Exp_msk1) {
  2027. if (L > (P+2)*Exp_msk1)
  2028. /* round even ==> */
  2029. /* accept rv */
  2030. break;
  2031. /* rv = smallest denormal */
  2032. goto undfl;
  2033. }
  2034. }
  2035. #endif /*Avoid_Underflow*/
  2036. L = (word0(rv) & Exp_mask) - Exp_msk1;
  2037. #endif /*Sudden_Underflow}}*/
  2038. word0(rv) = L | Bndry_mask1;
  2039. word1(rv) = 0xffffffff;
  2040. #ifdef IBM
  2041. goto cont;
  2042. #else
  2043. break;
  2044. #endif
  2045. }
  2046. #ifndef ROUND_BIASED
  2047. if (!(word1(rv) & LSB))
  2048. break;
  2049. #endif
  2050. if (dsign)
  2051. dval(rv) += ulp(rv);
  2052. #ifndef ROUND_BIASED
  2053. else {
  2054. dval(rv) -= ulp(rv);
  2055. #ifndef Sudden_Underflow
  2056. if (!dval(rv))
  2057. goto undfl;
  2058. #endif
  2059. }
  2060. #ifdef Avoid_Underflow
  2061. dsign = 1 - dsign;
  2062. #endif
  2063. #endif
  2064. break;
  2065. }
  2066. if ((aadj = ratio(delta, bs)) <= 2.) {
  2067. if (dsign)
  2068. aadj = dval(aadj1) = 1.;
  2069. else if (word1(rv) || word0(rv) & Bndry_mask) {
  2070. #ifndef Sudden_Underflow
  2071. if (word1(rv) == Tiny1 && !word0(rv))
  2072. goto undfl;
  2073. #endif
  2074. aadj = 1.;
  2075. dval(aadj1) = -1.;
  2076. }
  2077. else {
  2078. /* special case -- power of FLT_RADIX to be */
  2079. /* rounded down... */
  2080. if (aadj < 2./FLT_RADIX)
  2081. aadj = 1./FLT_RADIX;
  2082. else
  2083. aadj *= 0.5;
  2084. dval(aadj1) = -aadj;
  2085. }
  2086. }
  2087. else {
  2088. aadj *= 0.5;
  2089. dval(aadj1) = dsign ? aadj : -aadj;
  2090. #ifdef Check_FLT_ROUNDS
  2091. switch(Rounding) {
  2092. case 2: /* towards +infinity */
  2093. dval(aadj1) -= 0.5;
  2094. break;
  2095. case 0: /* towards 0 */
  2096. case 3: /* towards -infinity */
  2097. dval(aadj1) += 0.5;
  2098. }
  2099. #else
  2100. if (Flt_Rounds == 0)
  2101. dval(aadj1) += 0.5;
  2102. #endif /*Check_FLT_ROUNDS*/
  2103. }
  2104. y = word0(rv) & Exp_mask;
  2105. /* Check for overflow */
  2106. if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
  2107. dval(rv0) = dval(rv);
  2108. word0(rv) -= P*Exp_msk1;
  2109. adj = dval(aadj1) * ulp(rv);
  2110. dval(rv) += adj;
  2111. if ((word0(rv) & Exp_mask) >=
  2112. Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
  2113. if (word0(rv0) == Big0 && word1(rv0) == Big1)
  2114. goto ovfl;
  2115. word0(rv) = Big0;
  2116. word1(rv) = Big1;
  2117. goto cont;
  2118. }
  2119. else
  2120. word0(rv) += P*Exp_msk1;
  2121. }
  2122. else {
  2123. #ifdef Avoid_Underflow
  2124. if (scale && y <= 2*P*Exp_msk1) {
  2125. if (aadj <= 0x7fffffff) {
  2126. if ((z = (ULong) aadj) <= 0)
  2127. z = 1;
  2128. aadj = z;
  2129. dval(aadj1) = dsign ? aadj : -aadj;
  2130. }
  2131. word0(aadj1) += (2*P+1)*Exp_msk1 - y;
  2132. }
  2133. adj = dval(aadj1) * ulp(rv);
  2134. dval(rv) += adj;
  2135. #else
  2136. #ifdef Sudden_Underflow
  2137. if ((word0(rv) & Exp_mask) <= P*Exp_msk1) {
  2138. dval(rv0) = dval(rv);
  2139. word0(rv) += P*Exp_msk1;
  2140. adj = dval(aadj1) * ulp(rv);
  2141. dval(rv) += adj;
  2142. #ifdef IBM
  2143. if ((word0(rv) & Exp_mask) < P*Exp_msk1)
  2144. #else
  2145. if ((word0(rv) & Exp_mask) <= P*Exp_msk1)
  2146. #endif
  2147. {
  2148. if (word0(rv0) == Tiny0
  2149. && word1(rv0) == Tiny1)
  2150. goto undfl;
  2151. word0(rv) = Tiny0;
  2152. word1(rv) = Tiny1;
  2153. goto cont;
  2154. }
  2155. else
  2156. word0(rv) -= P*Exp_msk1;
  2157. }
  2158. else {
  2159. adj = dval(aadj1) * ulp(rv);
  2160. dval(rv) += adj;
  2161. }
  2162. #else /*Sudden_Underflow*/
  2163. /* Compute adj so that the IEEE rounding rules will
  2164. * correctly round rv + adj in some half-way cases.
  2165. * If rv * ulp(rv) is denormalized (i.e.,
  2166. * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
  2167. * trouble from bits lost to denormalization;
  2168. * example: 1.2e-307 .
  2169. */
  2170. if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
  2171. dval(aadj1) = (double)(int)(aadj + 0.5);
  2172. if (!dsign)
  2173. dval(aadj1) = -dval(aadj1);
  2174. }
  2175. adj = dval(aadj1) * ulp(rv);
  2176. dval(rv) += adj;
  2177. #endif /*Sudden_Underflow*/
  2178. #endif /*Avoid_Underflow*/
  2179. }
  2180. z = word0(rv) & Exp_mask;
  2181. #ifndef SET_INEXACT
  2182. #ifdef Avoid_Underflow
  2183. if (!scale)
  2184. #endif
  2185. if (y == z) {
  2186. /* Can we stop now? */
  2187. L = (Long)aadj;
  2188. aadj -= L;
  2189. /* The tolerances below are conservative. */
  2190. if (dsign || word1(rv) || word0(rv) & Bndry_mask) {
  2191. if (aadj < .4999999 || aadj > .5000001)
  2192. break;
  2193. }
  2194. else if (aadj < .4999999/FLT_RADIX)
  2195. break;
  2196. }
  2197. #endif
  2198. cont:
  2199. Bfree(PASS_STATE bb);
  2200. Bfree(PASS_STATE bd);
  2201. Bfree(PASS_STATE bs);
  2202. Bfree(PASS_STATE delta);
  2203. }
  2204. #ifdef SET_INEXACT
  2205. if (inexact) {
  2206. if (!oldinexact) {
  2207. word0(rv0) = Exp_1 + (70 << Exp_shift);
  2208. word1(rv0) = 0;
  2209. dval(rv0) += 1.;
  2210. }
  2211. }
  2212. else if (!oldinexact)
  2213. clear_inexact();
  2214. #endif
  2215. #ifdef Avoid_Underflow
  2216. if (scale) {
  2217. word0(rv0) = Exp_1 - 2*P*Exp_msk1;
  2218. word1(rv0) = 0;
  2219. dval(rv) *= dval(rv0);
  2220. #ifndef NO_ERRNO
  2221. /* try to avoid the bug of testing an 8087 register value */
  2222. if (word0(rv) == 0 && word1(rv) == 0)
  2223. errno = ERANGE;
  2224. #endif
  2225. }
  2226. #endif /* Avoid_Underflow */
  2227. #ifdef SET_INEXACT
  2228. if (inexact && !(word0(rv) & Exp_mask)) {
  2229. /* set underflow bit */
  2230. dval(rv0) = 1e-300;
  2231. dval(rv0) *= dval(rv0);
  2232. }
  2233. #endif
  2234. retfree:
  2235. Bfree(PASS_STATE bb);
  2236. Bfree(PASS_STATE bd);
  2237. Bfree(PASS_STATE bs);
  2238. Bfree(PASS_STATE bd0);
  2239. Bfree(PASS_STATE delta);
  2240. ret:
  2241. if (se)
  2242. *se = (char *)s;
  2243. return sign ? -dval(rv) : dval(rv);
  2244. }
  2245. static int
  2246. quorem
  2247. #ifdef KR_headers
  2248. (b, S) Bigint *b, *S;
  2249. #else
  2250. (Bigint *b, Bigint *S)
  2251. #endif
  2252. {
  2253. int n;
  2254. ULong *bx, *bxe, q, *sx, *sxe;
  2255. #ifdef ULLong
  2256. ULLong borrow, carry, y, ys;
  2257. #else
  2258. ULong borrow, carry, y, ys;
  2259. #ifdef Pack_32
  2260. ULong si, z, zs;
  2261. #endif
  2262. #endif
  2263. n = S->wds;
  2264. #ifdef DEBUG
  2265. /*debug*/ if (b->wds > n)
  2266. /*debug*/ Bug("oversize b in quorem");
  2267. #endif
  2268. if (b->wds < n)
  2269. return 0;
  2270. sx = S->x;
  2271. sxe = sx + --n;
  2272. bx = b->x;
  2273. bxe = bx + n;
  2274. q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
  2275. #ifdef DEBUG
  2276. /*debug*/ if (q > 9)
  2277. /*debug*/ Bug("oversized quotient in quorem");
  2278. #endif
  2279. if (q) {
  2280. borrow = 0;
  2281. carry = 0;
  2282. do {
  2283. #ifdef ULLong